up previous next

Hilbert-Driven Computations

CoCoA Groebner basis algorithms will use knowledge of a Poincare series to improve efficiency.

example

    
Use R ::= Q[w,x,y,z];
PS := HP.PSeries(1 + 2w + 3w^2 + 4w^3 + 5w^4 + 6w^5 + 5w^6 +
 4w^7 + 3w^8 + 2w^9 + w^10,2);
PS;
(1 + 2w + 3w^2 + 4w^3 + 5w^4 + 6w^5 + 5w^6 + 4w^7 + 3w^8 + 2w^9 + w^10) / (1-w)^2
-------------------------------
I := Ideal((xy-zw)^3,(xz-yw)^3);
I.PSeries := PS; -- this is how to let CoCoA know about the Poincare series
G := GBasis(I);